Calculate Scalar Product for Vectors M and N in Cartesian XY System

[runner1738]

Consider the two vectors M =(a,b) = ai+bj and N = (c,d) = ci +dj, where a =4, b =4, c = -1, and d = 1. a and c represent the x-displacment and b and d represent the y-displacment in a Cartesian xy co-ordinate system.
Note: i and j represent unit vectors(i.e. vectors of length l)in the x and y directions, respectively. what is the value of the scalar product N x N?

 

[vsage]

Do you know the definition of the scalar product? It's just the product of each i component + the product of each j component.

 

[runner1738]

but then wouldn't that be (4,-1)+(4,1) so you get (-3) +(5)

 

[vsage]

Sorry I should have specified:

If you have 2 vectors in the form ai + bj and ci + dj, you obtain the scalar product by multiplying a by c and b by d to obtain ac + bd. You multiply each component separately before adding.

 

[Nylex]

but then wouldn't that be (4,-1)+(4,1) so you get (-3) +(5)

I assume by (4, -1) you mean 4 x -1, but where did that -1 come from?

You should also know that the scalar product, a.b = |a||b|cos theta, where theta is the angle between a and b. From that, you should be able to see what the scalar product of n with itself is.

 

[runner1738]

c=-1, so -4 + 4 =0 , so your saying i have to solve for the angle in betwwen first, which can be easily done?

 

[vsage]

It's not necessary here but if you're ever given a question like "Magnitude of A is x and Magnitude of B is y and the angle between them is t degrees find A dot B" you know how to apply it.

 

[runner1738]

well zero isn't the answer

 

[vsage]

what is the value of the scalar product N x N?

Are you sure that's written correctly? It looks like it's asking you to take the dot product of a vector with itself. Additionally, N x M is usually the convention for the vector product (cross product). Can you confirm the question is worded exactly like in the quotes?

 

[runner1738]

yea on the homework the question is what is the value of the scalar product N <dot> N? is it a trick question or something

 

[vsage]

It was a trick. Vector M is irrelevant. Just take the dot product of N with itself (-1*-1+1*1)

 

[runner1738]

correct thank you so much, but what if i do need M dot N

 

[vsage]

Just multiply the i component of N and the i component of M together then sum it to the product of the j component of N and the j component of M